Tail expansions for random record distributions

Abstract

The random record distribution ν associated with a probability distribution μ can be written as a convolution series, ν = Σn=1∞(n + 1)-1μ(Black star)n. Various authors have obtained results on the behaviour of the tails ν((cursive Greek chi, ∞)) as cursive Greek chi → ∞, using Laplace transforms and the associated Abelian and Tauberian theorems. Here we use Gelfand transforms and the Wiener-Lévy-Gelfand Theorem to obtain expansions of the tails under moment conditions on μ. The results differ notably from those known for other convolution series. © 2001 Cambridge Philosophical Society.